PROBABILITY GEOMETRY B
COMPREHENSIVE EXAMINATION
PROBLEMS AND VERIFIED ANSWERS
BUNDLED
●● Given △ABC, sin(A) =
Answer: cos(c)
●● To support a tree damaged in a storm, a 12-foot wire is secured from
the ground to the tree at a point 10 feet off the ground. The tree meets
the ground at a right angle.
At approximately what angle does the wire meet the ground?
Answer: 56.4°
●● Given △ABC ~ △XYZ, what is the value of cos(Z)?
Answer: 12/13
●● The equation tan(55°) = 15/b can be used to find the length of AC.
,What is the length of AC? Round to the nearest tenth.
Answer: 10.5
●● Given right triangle QRS, what is the value of sin(30°)?
Answer: 1/2
●● The equation cos(35°) = a/25 can be used to find the length of BC.
What is the length of BC? Round to the nearest tenth.
Answer: 20.5
●● The longest side of an isosceles obtuse triangle measures 20
centimeters. The other two side lengths are congruent but unknown.
What is the greatest possible whole-number value of the congruent side
lengths?
Answer: 14 cm
●● Kari is flying a kite. She releases 50 feet of string. What is the
approximate difference in the height of the kite when the string makes a
,25o angle with the ground and when the string makes a 45o angle with
the ground? Round to the nearest tenth.
Answer: 14.2 feet
●● Building A and building B are 500 meters apart. There is no road
between them, so to drive from building A to building B, it is necessary
to first drive to building C and then to building B.
About how much farther is it to drive than to walk directly from building
A to building B? Round to the nearest whole number.
Answer: 183 meters
●● Which equation can be used to find the measure of angle LKJ?
Answer: sin-1(8.9/10.9) = x
●● Which is the best approximation for the measure of angle ABC?
Answer: 58.3°
●● A theater production group is making frames to support wall-like
props. Three-foot beams form right triangles with 10-foot beams to
allow them to stand, as shown in the image.
, What is x, the angle at which the diagonal beam meets the 10-foot beam
at the top of the frame?
Answer: 16.7°
●● Two sides of an acute triangle measure 5 inches and 8 inches. The
longest side is unknown.
What is the greatest possible whole-number length of the unknown side?
Answer: 9 inches
●● Jamel is asked to create triangles using three of four given sticks.
The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4
triangles.
Triangle 1: 3 in., 6 in., 7 in.
Triangle 2: 3 in., 6 in., 8 in.
Triangle 3: 3 in., 7 in., 8 in.
Triangle 4: 6 in., 7 in., 8 in.
How many of his triangles are obtuse?
Answer: 3
COMPREHENSIVE EXAMINATION
PROBLEMS AND VERIFIED ANSWERS
BUNDLED
●● Given △ABC, sin(A) =
Answer: cos(c)
●● To support a tree damaged in a storm, a 12-foot wire is secured from
the ground to the tree at a point 10 feet off the ground. The tree meets
the ground at a right angle.
At approximately what angle does the wire meet the ground?
Answer: 56.4°
●● Given △ABC ~ △XYZ, what is the value of cos(Z)?
Answer: 12/13
●● The equation tan(55°) = 15/b can be used to find the length of AC.
,What is the length of AC? Round to the nearest tenth.
Answer: 10.5
●● Given right triangle QRS, what is the value of sin(30°)?
Answer: 1/2
●● The equation cos(35°) = a/25 can be used to find the length of BC.
What is the length of BC? Round to the nearest tenth.
Answer: 20.5
●● The longest side of an isosceles obtuse triangle measures 20
centimeters. The other two side lengths are congruent but unknown.
What is the greatest possible whole-number value of the congruent side
lengths?
Answer: 14 cm
●● Kari is flying a kite. She releases 50 feet of string. What is the
approximate difference in the height of the kite when the string makes a
,25o angle with the ground and when the string makes a 45o angle with
the ground? Round to the nearest tenth.
Answer: 14.2 feet
●● Building A and building B are 500 meters apart. There is no road
between them, so to drive from building A to building B, it is necessary
to first drive to building C and then to building B.
About how much farther is it to drive than to walk directly from building
A to building B? Round to the nearest whole number.
Answer: 183 meters
●● Which equation can be used to find the measure of angle LKJ?
Answer: sin-1(8.9/10.9) = x
●● Which is the best approximation for the measure of angle ABC?
Answer: 58.3°
●● A theater production group is making frames to support wall-like
props. Three-foot beams form right triangles with 10-foot beams to
allow them to stand, as shown in the image.
, What is x, the angle at which the diagonal beam meets the 10-foot beam
at the top of the frame?
Answer: 16.7°
●● Two sides of an acute triangle measure 5 inches and 8 inches. The
longest side is unknown.
What is the greatest possible whole-number length of the unknown side?
Answer: 9 inches
●● Jamel is asked to create triangles using three of four given sticks.
The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4
triangles.
Triangle 1: 3 in., 6 in., 7 in.
Triangle 2: 3 in., 6 in., 8 in.
Triangle 3: 3 in., 7 in., 8 in.
Triangle 4: 6 in., 7 in., 8 in.
How many of his triangles are obtuse?
Answer: 3
